Classical electron uncertainty

[AndreiB]

In quantum mechanics it is impossible to prepare an electron in a state where both position and momentum are known with arbitrary accuracy. In classical physics such states do exist, but can they be prepared?

If we assume that the electron is a classical particle (small ball of charge) can we imagine an experiment, consistent with the laws of classical electromagnetism, that leaves the electron with a arbitrarily well known position and momentum?

 

[vanhees71]

Sure, why not?

 

[AndreiB]

Sure, why not?

Can you provide an example?

 

[vanhees71]

In classical electron theory you describe point particles as points in phase space as any classical point-particle theory. It's of course evident that this is an approximation, and there is no fully consistent relativistic dynamics of interacting point particles. The best you can come up with, using quantum theory of open systems (quantum Langevin equations), is an effective theory which boils down to the Landau-Lifshitz equation of motion. See, e.g.,

G. W. Ford et al, Phys. Rev. A 37, 4419 (1988)

 

[AndreiB]

In classical electron theory you describe point particles as points in phase space as any classical point-particle theory. It's of course evident that this is an approximation, and there is no fully consistent relativistic dynamics of interacting point particles. The best you can come up with, using quantum theory of open systems (quantum Langevin equations), is an effective theory which boils down to the Landau-Lifshitz equation of motion. See, e.g.,

G. W. Ford et al, Phys. Rev. A 37, 4419 (1988)

As far as I know, Born-Infeld theory is consistent. But is it really necessary to think of an experiment in the relativistic regime?

 

[vanhees71]

I'm not sure, but isn't Born-Infeld theory ruled out by experiments?

 

[AndreiB]

I'm not sure, but isn't Born-Infeld theory ruled out by experiments?

I don't know about that, but it does not matter. It's a thought experiment. Let's assume, for the sake of the argument that the theory is true. Can you imagine an experiment that allows you to prepare an electron with accurately known position and momentum?

 

[Vanadium 50]

Put the electron in a trap and let it radiate away its energy until it has stopped in the center of the trap. Done.

 

[AndreiB]

Put the electron in a trap and let it radiate away its energy until it has stopped in the center of the trap. Done.

What kind of trap?

 

[Vanadium 50]

An electron trap.

 

[AndreiB]

An electron trap.

If you are referring to a Penning trap, the electron does not remain stationary in the middle.

 

[Vanadium 50]

Paul trap, Penning trap whatever.

the electron does not remain stationary in the middle.

And why? Quantum mechanics!

In a Penning trap, typically the cyclotron motion is in its ground state. It has energy ½ħω which it can't radiate away. Because of quantum mechanics.

Classically, it can have any energy it wants and will radiate it away until it is arbitrarily close to zero.

 

[AndreiB]

In a Penning trap, typically the cyclotron motion is in its ground state. It has energy ½ħω which it can't radiate away. Because of quantum mechanics.

Classically, it can have any energy it wants and will radiate it away until it is arbitrarily close to zero.

In this paper the particle motion in a penning trap is treated classically:

Penning traps as a versatile tool for precise experiments in fundamental physics
K. Blaum, Yu.N. Novikov, G. Werth
Contemporary Physics, 51: 2, 149 -- 175 (2010)

https://arxiv.org/abs/0909.1095

At page 6 we read:

" we obtain three independent motional modes as shown in figure 3: (i) a harmonic oscillation along the z-axis with frequency ωz, (ii) a circular radial cyclotron motion with frequency ω+ slightly reduced compared to the free particles cyclotron frequency ωc and (iii) a circular radial magnetron or drift motion at the magnetron frequency ω- around the trap center."

So, even classically, the particle will move inside the trap. I guess that the energy of the particle is taken from the external fields, this is why the particle does not stop.

 

[Vanadium 50]

That paper does not support your point.
It's not nice to post a 78-page paper that ends up not supporting your point.

For the third time, classical motion produces classical radiation, which causes energy loss, slowing the particle. The paper itself shows this energy loss in equation (21), so it is kind of disingenuous to pretend it doesn't exist.

 

[fresh_42]

The topic in this thread is not really EM. It is how to shoot entire QM with one bullet from behind through the back into the eye.

Please remember that our credo is "Science as taught at universities."

This thread is closed.